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COLOROID SYSTEM

By

A. NE;\ICSICS

Department of Drawing and Composition, Technical University, Budapest Received: July 17, 1978

Introduction

For the architect dcsigning coloured enTironment, colour may be botH a technical and an artistic means. In the first case the possibility to define technical parameters assigned to different colours, in the latter case, to express the compositional relations between colours by numbers requires to identify each member of the group of colours by indices. Both requirements relate the prohlem of colour notation to that of colour systematization. The relation between the millions of distinct colours in the set and their indices cannot be an accidental one, hut has to rely on colour systematization.

Many colour experts couple the concept of colour systematization almost entircly to colorimetry ([1] to [5]).

According to the well-known wording hy G. "",VX-SZECKI [6], colorimetry is a means for predicting if t·wo yisual stimuli of different 8pectral distribution will produce the same colour sensation uncleI' giyen conditions, by predicting the place of the two yisual stimuli in a giyen colour space. If the colour-space co-ordinates of OIle stimulus equal those of the other one, a person with normal colour yision will feel the two colours to be equal.

This means is increasingly applied in modern industry, among others for numerically settling the difference hetween two colours. The endeavour to express the rate of change in colour perception by a proportionalnumcrical change of colour indices has actually becomc the most important criterion of qualifying the colour systcms.

For colour dynamics, the scicnce of colour spacc design, to possess colour indices for numcrically descrihing colour compositions has become a technical necessity hy no·w, changing, however, the requirements for colour systems. This paper is going to deal with thcse new requirements as well as with the COLOROID colour system elaborated to meet them.

ReseaTeh work in connection with the COLOROID coluur system has been carried on since 1962 at the Technical University, Budapest. The work 'was s1 :ll'ted by creating differcnt aesthetically~ uniform psycho-mctric scales, that

3*

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36 NEMCSICS

is, those felt to be uniformly varying when considered as a whole. "Considered as a whole" means that test subjects rated e.g. the brightness scale of about 20 to 100 members from white to black by viewing it at once, without con- centrating on the relation between neighbouring colours in a section of the scale. The number of colours between each two colours of the scale was evenly increased up to a density whele two adjacent colours could not be used any- more in a colour harmony design. The difference between these colours was named harmony interval. The number of harmony intervals between two neigh- bouring members of aesthetically uniform scales was found everywhere equal, contrary to the perception ally even steps.

Scoring by over 70 thousand persons was used when creating the scale.

Most of our results have been published successively [7-21]. During this work, our conception of the colour space of this colour dynamic system has been gradually modified. Thus, the set of our publications does not sho·w the details but the different phases of development of the COLOROID. This is the first attempt to present in full the experiments made for creating the system, its interrelations and their application for colour composition.

1. The requirements of colour dynamics for colour systematization The basic problem of colour systematization is rooted in the subjective colour perception, which is the result of highly compounded effects. It depends on the spectral energy distribution of the light source illuminating the coloured surface to be observed, on the luminance factor of the surface, on the geometry of observation and reflexion. Thus, in order to unambiguously express a colour perception, the spectral energy distribution of the light source, the luminance factor of the surface to be observed, and the geometry of observation and illu- mination have to be fixed.

Also the characteristics of the colour perception mechanism influence the colour sensation. Estimation of a colour is also affected by factors such as the chromatic adaptation, the chromatic constancy, the phenomenon of colour contrast and the fatigue of the eyes. Therefore, in defining a colour also its environment, the duration of observation, the state of the chromatic adaptation have to be fixed.

Besides, the colour sensation depends on the age, temperament, educa- tion, etc. of the viewer, therefore colour sensation grades can only be formed by statistically averaging the opinion of a great number of observers.

In the following we intend to enumerate the requirements of colour dynamics poi 1.ting beyond the general problems of colour systematization.

Both the discussion and the conclusion will be facilitated by being definitely referred to the Munsell and the COLOROID colour systems.

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1.1 Indices expressing the three characteristics of visual sensation: hue saturation and brightness

In different colour systems, colour indices are assigned to different num- bers of colour samples. In the Munsell and COLOROID colour systems, simil- arly to other colour systems, these colour indices signify not only the place of the sample within the collection but also the relative values of the three char- acteristics of visual sensation: hue, saturation and brightness.

This is very important for colour dynamics. In everyday life we remember or describe a colour by these three qualities. Any difference or similarity in them induces us to speak of a colour different from or similar to another colour.

Also aesthetical decisions, e.g. whether a colour composition is harmonious or disharmonious are made according to differences felt bet"ween colour char- acteristics.

1.2 Indices expressing the aesthetical continuity of the colour space

Colour sensations are not physical quantities to be characterized by physical units, but to be expressed by the change of the three colour sensation qualities in a given numerical range in both colour systems. Each colour sensation series consisting of colours evenly changing in relation to a certain quality is expressed by different colour index series in the two colour systems.

Let us compare them.

The two colour sensation indices can only be compared by relating indices assigned to colour sensations produced by defined stimuli. Brightnesses and saturations in the two colour systems are related by:

Vc = 10 V1.2219V m - 0.23111 V~

+

0.23951

Pm -

0.021009V~

+

0.0008404V~

and 3

T = ab

VC

2

respectively, where Vc and V m express COLOROID and lVIunsell brightnesses, T is saturation in the COLOROID system, C the lVIunsell-chroma; a and b in the second formula mean that the assignment of both COLOROID and lY.lunsell indices to the saturation of a colour depends also on its brightness and hue.

The formulae show that to sensations elicited by identically changing stimuli, a set of indices changing according to a different law is assigned in each system. Thus, the two systems suggest different ways of measuring the colour sensation. Let us compare the two suggestions to see which one suits better the requirements of colour dynamics.

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38 iYE}lCSICS

In the ]Hu1Zsell system a colour series evenly changing from the aspect of a certdn parameter was developed with approximately equal, small colour differences between its members what meallS that between each index approx- imately the same number of shades can be distinguished. This characteristic of the i1;lullseiZ system for describing colour differences has become increasingly important with the development of colour measurement.

It is undoubtedly important also for colour dynamics to fix ho'w much the actual colour may be aIlo'wed to differ from the planned one. However, the particular colour dynamic prohlems arise beyond this field, referring to colour-compositional relationships to he fixed by colour indices.

The colours of our environment belong to various parts of the colour space. Therefore the planning of a coloured environment has to bring about harmony of hue, saturation and hrightness between highly different colours.

This is -why far greater importance is due to the aesthetical evenness of the whole colour space than to the reliable equality of small colour differences.

The endeavours of colour systematization resulting in the present form of the klullsell colour system produced psycho-physical scales fairly approximating the ability of the human eye to distinguish colours in various ranges hut little suiting aesthetical applications.

In our experiments to be presented later, we found that in the klu1Zsell system the brightness gradation of the colours -was denser for dark colours than 1\-ould he required byaesthetical evenness. In spite of the almost equal colour differences, the saturation steps were found to be aesthetically denser in dark areas of the colour solid than in bright ranges. Furthermore, the jHu1Zsell chroma steps were found in the highly saturated fields to be aesthetically far too scarce, whereas in the unsaturatcd fields far too dense.

To be concise, according to the second requirement of colour dynamics for colour systems, the index yariation IW5 to follow an aestlwtically eyen yariation of colour5. This means that the requiremcnts of colour dynamics arc met hy a colour space built on .. ,esti1l'ticdly equal colour cliffCTellccs, i.e.

where large (rather than small) colour dif[(TenCe5 are equal. The colour "pace of COLOROID has been elahorated :::ceordingly.

1.3 VisuaZi:;ing the colour by indices

Two colours and their mixing rates are glyen, the colour re:oulting from their mixing has to he determined. In colour ellyironm.ent design this task is quite frequent, e.g. when a third, harmonious colour is looked for to match t-wo giyen colours.

The indices in the Ilill1Zsell system aTe of no help, they being 1Il no direct relationship to the colour stimuli, phY3ical quantities eliciting colour sensation.

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The situation is quite different "with the CIE XY Z system "where for additive colour mixing the co-ordinates of the new colour can be determined.

The tristim1l1us value Y changes linearly with the mixing rate of the tristimu- Ius values Y of the colours to he mixed. On the other hand, the co-ordinates x and ). shift towards the colour with the high~r sum of tristimulus values.

The point plotting the resulting colour is OIl the straight line bet"ween the two starting colour points. Its position on this line is in proportion of the two sti- muli, if the sums of the tristimulus values of the colours are equal.

This is an cxact determination of the co-ordinates of thc mixed colour in the CIE system. But these co-ordinates still fail to indicate the saturation of our ne"w colour. Its direct visualization is still a problem.

Coloured environment design will profit from the definition of colour- mixing hy colour indices only if these suit numerical evaluation of the compo- sitional e.g. harmonic relation between the new colour and the component colours. Another aim of colour indices is to simplify visualization of the theor- etically mixed colour. The COLOROID colour indices can easily be converted to colour-mixing components for visualizing the colour.

1.4 Conversion of indices into the CIE XYZ system

The work of a colour designer is affected not only by exigencies but also hy external features, such as the colours of building and decorating materials, often indicated only hy their XYZ values by the manufacturer. The colour designer can make use of thesc data only if they can be cOllverted into indices involved in his theoretical-practical composition. As his conceptions have often to be agreed with the choicc of colours, a :::imple mcans of conversion is needed.

As the work of architects, interior designers and artists cannot be aided in the foreseeuhb future hy large computers, they must r21y for the conversion on small calcubtors, mayhe on graphic construction.

These statements raise the fourth re quiremcnt of colour dynamic::: for colour : direct COll"vr:rsioll of colour indiccs into CIE XY Z values and vice-ycna, hence a mutually unambiguous relation between the two colour spaces of COLOROID and CIE XYZ is needed. COLOROID has heen an attempt to fulfill this requirement.

2. Experiments for defining the COLOROID colour space

Colour points in a colour space representing colour perceptions form an aesthetically even relation only if the colour point indices suit to describe aesthetic relations of e.g. colour eomposition or colour hanllony.

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40 NEMCSICS

It was attempted to fulfill these requirements with the COLOROID system. Colour-bearing surfaces of our environment contain simultaneously a great variety of colours with different hues, saturations and brightnesses.

These colours are selected by the designer so as to be aesthetically related, thus pleasant to the eyes. The colours are easier to match if their aesthetic content varies in parallel to the indices, namely if the colours in a scale seen at once are of an aesthetically even gradation. The difference between the adjacent members of such a scale is that smallest interval by which a colour has to be altered to form a harmonious composition together with the original colour. This interval is not simply a multiple of the just noticeable colour differ- ence but depends on the brightness and saturation as well.

The hue, saturation and brightness scales of COLOROID have been established experimentally.

The experiments were performed in a room, near to the window looking north. Illumination on the test samples was 1600 to 1800 Ix.

Test subjects were male and female university students 19 to 23 years old.

Some experiments were repeated with pupils of elementary schools and with adults.

Test samples 15 to 18 cm2 in area lay on a horizontal surface and were lit by the light incident through the window at an angle of about 45°. Obser- vation angle was 90°, observation distance 100 cm.

The surrounding of the test field ",ras neutral gray, and no coloured light was reflected to the samples. Before tests, the subjects spent at least five minutes in the experimenting room to have their eyes adapted to the neutral environment. The time for choosing from among the colour samples and arranging them into harmonious scales was not confined.

2.1 Experiments for determining the relationship between hue and dominant wavelength

For a simple correlation with the CIE XY Z system, hues were identified by dominant wavelengths. Therefore the statement found in the literature and involved in establishing the Munsell system that the dominant wavelength changes with saturation and brightness has been checked in two test series.

In the first series the observers had to estimate the hue of samples repre- senting Munsell hues of 2.5 G, 2.5 Y, 2.5 R, 2.5 P and 2.5 B. As no original lliunsell samples were at our disposal, some 1000 samples "were prepared for each of the five hues above, their tristimulus values measured, and carefully selected for the lVIunsell scales.

The samples corresponding to the hue of 2.5 G had the widest scatter of dominant wavelength (526 to 540 nm), therefore the problem is best illustrat- ed by this experiment.

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The observers were presented the appropriate green colour series consist- ing of 15 samples. The 7th sample of the series had Munsell co-ordinates 2.5 G 4/4, its dominant wavelength was 533 nm. Two neighbouring samples were of the same chroma and value, but their hue changed into yellowish and bluish to the right and to the left, resp. The hue difference between two adjacent samples corresponded to a dominant wavelength difference of 2 nm.

The 1250 test subjects, 20 to 22 years of age and of about equal sex distribution had to match 70 samples with a hue of 2.5 G, but with different chroma and brightness values one by one to the hue of one chip of the sample series. Results of dominant wavelength vs. Munsell value, and dominant wave- length vs. 1'dunsell chroma are seen in Figs 1 and 2, resp. A single point averages 8 to 10 votes in the figure!';. The continuous lines are those corresponding to constant Munsell hue. The follo'wing conclusions were drawn from the experi- ments:

1. Not a single person gave answers in perfect agreement with the Munsell arrangement for all colours.

2. Only 5% of the observers answered correctly for more than 50% of the samples.

3.75% of the observers ranged 80% of the samples in the wavelength band LlH (see Figs 1 and 2) in an order exhibiting very low correlation between the Munsell sample order and the answers.

In the second experiment two compositions were shown the observers for choosing the more harmonious one, or for indicating if both compositions were found equally harmonious.

Both compositions consisted of 10 colours. One composition "A" con- sisted of Munsell hues 2.5 G 8/4-, 8/2, 6/8, 6/6, 4/6, 4/4, 4/2, 2/2 with dominant wavelengths ranging from 526 to 540 nm.

Tbe colours of composition "B" had only dominant wavelengths of about 533 nm. Brightnesses and chromas equalled those in composition" A", and so did the arrangements and frequencies of occurrence.

The same experiment was repeated with 1vlunsell hues 2.5 Y, 2.5 R, 2.5 G and 2.5 B.

The results of these experiments can be summarized as follows:

1. 68 % of the observers found no aesthetic difference between the two compositions.

2. 17% of the observers preferred composition "B", 15% composition "A"

These experiments permitted to conclude on the aesthetic irrelevance of reckoning with Munsell's suggestion of the hue sensation to vary for the same dominant wavelength but varying saturation and brightness in establish- ing the hue scale. Laics were even found to have difficulties with establishing this change in dominant wavelength.

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.YE.1ICSICS

525 522 519

513

510 2 3 4 5 6 7 8 9 10 V I

..

Fig. 1. Relationship between hue and dominant wavelength based on experiments on samples

!L. of JIunscll hue 2.5 G, represented as dominant wavelength vs. J[uf!sell valne

5"1Q ~

25 24 222013 16 14 1210 8 6 4 2 C

Fi!!. 2. Relationshin between hue and dominant wavclen!!th based on eXDeriments on samples

C of J[ullsell hue 2.5 G, represented as dominant w'~velength n. Jfil71Sell chroma -

2.2 Experiments Oll an aesthetically even hue scale

From our colour sample collection, 150 samples ,\Trn Jhmsell chr'oma values of 6/12, but with varying huC's have been selected.

The test subjects had to build up a coloUl' circle with 50 samples chosen and arranged so as to show even steps in hue, if the entire colour circle 'was vieweel simultaneously.

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The hue differences between two adjacent samples of this circle were regarded as aesthetically equal hue interyals and de~lOted by JA. Test results were summarized by determining the number of hue interyals £lA in eyery 10 nm dominant 'wayelength interyal between 400 to 700 nm and (-490) to (-570) nm. The equation of the ern-elope curye would relate the dominant wayelength to the aesthetically eyen hue scale. After somc trials, mathematical expression of the cun-e 'was found to be too complicated and unpractical.

Therefore the relation hetween the COLOROID hue scale and the dominant wayelengths has heen tabulated. Linear interpolation hetween the 48 points set out as hasic colours was found to he adequate for all practical purposes (Fig. 3).

Mi

6

5

"

:

"

3

. .

'

. .

.

2 '

.

Fig. 3. Ae~thetically even hue differences vs. dominant wavelength from experiment series on Jlunsell hue 2.5 G samples with VIC = 6/12 ratio

2.3 Experiments on the aesthetical eL'elmess of the saturation scale

- As a first step, experiments were carried out usiu!:!: JIllnscll colour samples. 6 to 10 further shades were painted between the following Jlunsell sample pairs:

For H = 2.5Y and v= 8, between C= 13, 16. 14. 12. 10. 3. 6. ,I, ::

for H 2.5Y and v= 6. between C= 14.12.10,8.6. ,I, ::

for H = 2.5B and v= 8. between C= 12,10,8.6, .1. 2 for H 2.5B and y= 6. between C= 16. 1·1. 12. 10. 8. 6. ,1. 2

for H = 2.5G and v= 3. between C= 22.20.18,16.1·1. 12, 10. 8. 6.4.2 for H 2.5G and v= 6. between C 26. 24. 22. 20. 18. 16, 1-1. 12,10.8. 6.4. 2 for H= 2.5R and V 8. between C= 10. 8. 6. 4. 2

for H 2.5R and V= 6. between C 18. 16. 1-1. 12. 10. 8. 6, 4. 2

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44 NEMCSICS

Fig. 4. Relationship between aesthetically even saturation differences .dT vs . . Munsell chroma C from lYIunsell sample experiment on the aesthetical evenness of the saturation scale

Thus 8 groups of 50 to 100 colour chips each were formed, with constant hue and value, but varying saturation (chroma) in each group. From each of these an arbitrary number of samples had to be selected, to build up scales of even saturation steps, when viewed simul- taneously.

The aesthetically equal saturation difference found between the adjacent samples was denoted by .dT. The number of steps .dT found between each two Munsell chroma steps was noted hy every observer. The evaluation of the experiments (see Fig. 4) resulted in the following equation:

V(L'.dT)3 = C (ab).

After the lY.runsell chroma scale turned out to be aesthetically uneven, a new experiment was launched: New groups of colour chips were produced as additive mixtures of chromatic samples of saturated blue, green, saturated warm yellow, saturated red ,~ith dominant wavelengths of 484, 520, 579 and 610 nm, resp., and achromatic white and black surfaces. The samples were attached to lW"axwell discs to exhibit various percentages of one chromatic and two achromatic surfaces. The perceived colour apparent on the rotating disc was reproduced by tempera paints.

Several thousand samples were prepared and those ~ith tristimulus values Y = 60 and Y = 30 selected.

The sample groups equal in hue and brightness but varying in saturation were presented to test subjects asked to select ten chips each and to order them into saturation scales seeming to vary uniformly if viewed simultaneously. It was found that in most cases the amount of colour needed for one saturation step to reach the next one was constant as an average (Fig. 5):

Therefore the COLOROID saturation concept was formulated as follows:

Colours are regarded as equally saturated if they can be produced by additively mixing the same percentage of saturated colour of the same dominant wavelength with white and black.

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T1

100

80

60

40

20

100-;

Fig. 5. Relationship between the COLOROID saturation scale aesthetically felt even and the COLOROID hue, from experiments on the aesthetical evenness of the saturation scale, made

on COLOROID samples with equal hue differences

2.4 Experiments on the aesthetic evenness of the brightness scale

Groups of colour chips for brightness scale experiments were generated in the following way: Additive colour mixes were prepared from a saturated colour, white and black at two saturation levels and different brightnesses by using ilfaxwell discs and were reproduced again by tempera painting.

The following saturated colours were used:

red x = 0.5675, y = 0.3221, Y

=

20.32 yellow x = 0.4627, y = 0.4685, Y = 66.32 green x = 0.2649, y = 0.4622, Y = 32.21 blue x = 0.1768, y = 0.2465, Y=17.81.

The saturated colours were used in the experiments in two proportions: they covered either 15% or 50% of the lYlaxwell disc, resulting in 8 groups of about 250 colours each of equal hue and saturation, but different brightness. Tristimulus values were measured and Y values recorded.

The 2800 observers, half men, half women, had to choose 20 samples from each group and to order them for decreasing brightness so that the scale should seem evenly darkening if viewed at once.

The brightness difference between two adjacent samples of a brightness scale was called aesthetic brightness interval and denoted by Ll V. The experi- ments were evaluated by counting the steps Ll V in each interval of 5 Y in the entire range from Y = 5 to Y = 80. Fig. 6 shows the results described by the equation:

(ELlV)2 =

Y.

\ 10

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46 SE.IIeSICS

2~~~~~~~~~~~~~.~

Y

Fig. 6. Relationship between an aesthetically even brightness seale and the eIE Y value from experiments on colour samples of various eIE Y values

Thus, an aesthetically eyen brightness scale is described better by a square root formula than by a cubic root one, inducing us to adapt the former for COLOROID.

The 111unsell gray scale of 20 elements has been compared with a 20- element brightness scale huilt on the principle of the square root formula.

The ohseryers found the square root scale aesthetically more eyen than the 111 llllsell one.

All the colour samples wcre measured three times by means of the MOMCOLOR tristimulus instrument of the Department of Dralcing and Com- position, and the results ·were ayeraged. From time to time control measurcmen t were performed on other instruments.

3. The COLOROID

The COLOROID system is built on. and mutually convertible with. -"

. .

the CIE XYZ system. The COLOROID indices have heen directly deduced from thc CIE tristimulus yalues, hut so as to df'fine perceptual COLOROID charac- tcristies; the COLOROID saturation, COLOROID brightllesE and COLOROID hue conccpts in good agreement with our colour perceptions. Colours haye heen arranged in COLOROID to raise the feeling of aesthetic eyenness in the ayerage man.

These statements mean that the empirical psychometric scales represent·

mg aesthetically uniform colour space needed to be adapted to CIE to cope

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with practical requircments. Hence, COLOROID is no ideal synthesis bctween aesthetically perfectly eycn perception and CIEbut a relation at the level of practical colour dynamics.

The striYe of COLOROID colour space to aesthetic eyenness does not rely on the Helmholtz idea of "yisually homogeneous colour space", so that his known tests for determining the line elements IH~Te not been involved in its deyelopment. Therefore the colour dynamically adequate COLOROID colour space is essentially different from transformations by CIE, UCS and, recently, by CIELAB and CIEL DV, coping ·with . colorimetry requirements, and also from the rhombohedral lattice system developed by OSA.

Because of the direct dependence on the CIE XYZ system, also COLO- ROID inyoh-es additiye colour mixing. Colours are considered to be mixes of the saturated basic colour, white and black, and the co-ordinates of the point representing the colour in the COLOROID system can be calculated from theEe components and their proportions.

COLOROID is essentially different from the OSTWALD system describ- ing colours by hue, white and black contents, in that its colour components determine perceptual features.

3.1 Description of the COLOROID system

COLOROID accommodates the three-dimensional set of colour percep- tions - as do most colour perception Eystems - in a cylindrical co-ordinate Eystem: hue yaries along the surface, saturation along the radius and brightness along the axis of the cylinder. Thus, achromatic colours from absolute black to ahsolute ·white are locatcd along this axis. Planes perpcndicular to this axis contain colours of equal hrightness. Further a-way from the axis, saturation increases. Colours of equal Eaturation are located on a cylindrical surface each.

Colours of equal hue are found on half-pl.mes cOlltaining the axis. The ahout elliptical outline of a skew section of the cylinder is the locus of the spectrum colours and the purples (limit colours). To 48 such limit colours, felt to be aesthetically eyen spaced, intcger numhers -wcre assigncd as indices, these han heen scttled as COLOROID hasic colours.

Eyery limit colour is connected to the absolute white and the ahsolute black by a boundary line, in thc plane defined by the aehromatie axis and the limit colour. Surfaces accommodating all the boundary lines form the COLO- ROID colour space (Fig. 7), a confined space that contains all perceptihle colours arranged according to the COLOROID perception system.

The achromatic axis of the COLOROID colour space has been diyided into 100 equal parts, and so arc the cylinder radii from the achromatic axis to the cylindrical surface of the colours. Diyisions represent aesthetically equal steps of saturation.

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48 NEMCSICS

Fig. 7. COLOROID colour space is a subspace containing all visible colours arranged accord- ing to the COLOROID perceptual system

The COLOROID colour space contains the COLOROID colour solid, locus of the surface colours (see Fig. 8). The most saturated colours of the COLOROID colour solid form a noncircular cylindrical surface.

Relation between the COLOROID and CIE XYZ systems can be visual- ized by drawing the COLOROID achromatic axis so as to coincide in an (x, y) diagram with the co-ordinates of CIE illuminant C. Half planes edging at the

Fig. 8. The COLOROID colour solid, part of the COLOROID space containing surface colours

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White

Black

Fig. 9. COLOROID colour planc outlincd by the achromatic axis and the boundary curves of the COLOROID colour space. Boundary curves of surface colours, cut out of the COLOROID

colours solid, are similar to, and located inside. the former

achromatic aXIS contain colours with equal COLOROID hue and constant CIE dominant or complementary wavelength.

The sections of the COLOROID colour space cut out by the half-planes are the COLOROID hue planes, confined by the achromatic axis and two limit curyes. The COLOROID hue and the dominant wavelength of each colour in a COLOROID hue plane are identical.

Curves of intersection between the COLOROID colour solid and the half-plane boundary curves of the surface colours are "imiiar to, and lay inside, the boundary curves (Fig. 9).

Points of any COLOROID section along lines paralh·l to the achromatic axis represent colours of equal COLOROID saturation, and pprpelldicular to them, of equal COLOROID brightness (Fig. 10).

vA

100 r--r--.-__

Fig. 10. Colours along straight lines parallel to the achromatic axis are of identical COLOROID saturation. Colours along straight lines perpendicular to them are of identical COLOROID

brightness 4 Periodica Polytechnic. A. 23/1

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50 NEMCSICS

While the configuration of a eOLOROID space section depends only on the brightness of the spectrum colour or purple on its tip, that of a eOLOROID solid section depends both on the eOLOROID brightll(,"~ and ,;atmation of the most "aturated surface colour in the plane (Fig. 11).

v&

100~1 ~:;~~~:;§§~::~~

20

30

40

~_---"50

Fig. 11. Various sections of the COLOROID colour space ana colour solid

8.2 Definitions in COLOROID

In eOLOROID, ('ycry coluur is regarded a,; an additiVf~ mixture of the specific limit colour, absolute white and ahsolute hlack. In the mixture the percentage of the limit eolour is d(;noted hy p, that of absolute white hy IV

and of absolute black IJY s; tllt's(' an' tht' tristimulus "values in the COLOROID system.

Tri;:timulus Yalw's of a colour ahnlYS add UJl to unity:

p-'-w+s=L (1)

Accordillgly, tlw XYZ tristimulu;.: ',"aIut's of a eOLOROID colour point.

can hc writtt'Il as :,lllU of the tristimulu,: values of th(~ limit colour, the absolut(~

white and tl[(~ ahsolntt' hlack. Thus:

X =pX,;.

+

wX\1' - sXs (2)

Y

=

pY;. wY1\' sYs (3)

Z =pZi. wZ\l' sZs (4 )

whcre X, Y, Z are thl' eIE tristimulus values of the given colour, X;., Yi., Zi.

those of the limit colour, X"" Y1\" Zn' and Xs , Ys, Zs thost' of ahsolutt' white and ahsolute black, re"p.

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Denoting out' per cent of tht~ sum of the tri::;timulu~ Yalu('s for a colour point by c, the hundl't'Clth part of th(' sum ofEqs (2), (3) and(4) can be written as:

Scs (5)

a eorl'l'llil'nt form of l'xpre~~ing the eOLOROID colour poinb as :sum of the eOLOROlD tri:::tilllulus yalue,;: hue content, whi.teness content and blackness content. In addition to repn-sl'uting eOLOROID colour points as additiye mixturt,s of tIll' limit colour, absolutt' white and absolute black, they can also be dt'scribed a~ additive mixtures of a colour of equal hue, hut higher satura- tion, and two achromatic colours, 0111: brighter, the other darker than the actual colour, if their eIE tristimulus yalues are known. Thus:

Pt

+

IVt -'- SI

=

1

11('n('(', ill eonformity with tht· COLOROID prineiple:

z

and thu~

(6)

(7) (8) (9)

(10) Tlu, limit eolonrs, th,· ah;:;oillt., whitt· and tlu~ absolute blaek han' heell elt'fined In· tllt'ir elE tristiIlluiu5 ';alu('s.

eOLOROID limit colours an' tll<' q)t'etrulll colours ranging from 450 IlIll

to 625 llIll ill ilu' (x, y) diagralll, as well as colours along the straight line conllecting them (Fig. 12). By ddinition these equal the eIE spectral tristimulus fU!lction~, proyided .1'(555) 100 ha~ heen cllO:oen, involYing

5V.)

V().) (yi"iiJility curyc). Theri'hy tht· brightness of the limit colours had hCPll defined. 1~ yalnes of the eOLOROID limit colours rang\' from 0 to 100 and equal hundred times the "Iwctral tristimulus function y().).

The spectral tri:;timullls funetioll:' of th!' COLOROID limit colours (Xi., .ri.' z?) and their sums

_ - Xi. Z,.

ci.

=

Xi.

+

Yi.

+

Zi.

= -'---

100

(11)

hayc heen talJUlatcd with 1 Hill "tq)s, hased on Table" 3.3 in [6]. In the rallge of purple colours the ,.ums of eIE tristimulus functiolls of the COLOROID limit colours have heen determined hy additively mixing hlue of },

=

450 Illll and red of ). = 625 mn. The limit points were at the intersection of the line

4*

(18)

52 IVEMCSICS

Fig. 12. Limit colours of COLOROID plotted in the CIE (xy) diagram

cOllllecting wavelengths of 450 and 625 nm and the lines incident to the CIE chromaticity point C at different slopes tg rp. The intersections were determined mathematically, using the f?quations of the lines.

Since the COLOROID saturation of a colour also dcpends OIl the sum of thc tristimulus values of the involved limit colour, tll(' too low CIE tri- stimulus values on the purple line inducpd us to assumc the COLOROID limit colours inside, rather than along, thl' CIE purple line. Otherwise, mixture:- with colours at or near the CIE pm'ple line would be rather unsaturated, en'Il short of medium saturation.

The light of CIE illuminant C reflected from a surface of a perfect diffuse reflector is regarded as absolute white. Its luminance factor Y

=

100 is in accord- ance with the Y values of the COLOROID limit colours. Onc hundredth of the sum of the tristimulus values of absolulp white referred to CIE standard illuminant C is

and

_X_T ':.:.-l' _ . _Y----"-w __ Z_,"-v

=

3 .16 2955 100

100.

(12) (13) The absolute black can he visualized hy illuminating a perfectly absorhing eavity with Q

=

0 by CIE standard illuminant C. The Cs value is thus

(14) and

Ys = O. (IS)

(19)

560

0.6 500 570

Fig. 13. Colours of identical COLOROID hue are along half lines starting from the colour point of CIE ,tandard illuminant C in the (xy) diagram

Thus, the absolute COLOROID hlack is at the intersection of the COLO- ROID neutral axis hy the plane Y

=

0 of CIE 1931, hf'ncf', in rase of a radial distribution C, its co-ordinates arc:

xs = xo = 0.31006 Ys Yo 0.31616.

The position of a colour point in the COLOROID colour space is given by its COLOROID co-ordinates, denoted by the symbols:

A COLOROID hue T COLOROID saturation

v =

COLOROID brightness.

Colours are of cqual COLOROID hue if they can be reproduced hy additively mixing a COLOROID limit colour, absolute white and absolute hlack. The COLOROID hue depends on the hue of the limit colour defined hy its dominant wavelength. Colours with equal COLOROID hue are on a half- line joining in the (x, y) diagram the chromaticity locus of CIE standard illuminant C with the chromaticity point of the given limit colour (Fig. 13).

The hue can also he given as the direction tangent to this line. Be rp the angle hetween this line and the horizontal, then the slope of the line is m = tg rp, thus:

A

=

f(rp); A

=

f(tg rp). (16)

(20)

54 NEMCSICS

Tht: COLOROID system in,-oIYe:' 4,8 ha:;ic hu(':> in corn-;::I)()ndcnce with the 48 hasic colours, with integer number:, a,; indict,:" TllI'se corrt':3pond to the wavelengths and direction tangent:> in Table 1, iIHlicatillg also the tristimulus yalue:-, chromaticity co-ordinatt'" and 8;. ,-alues of the COLOROID hasie colours.

Hues lying bet-ween the basie ont'S art' denoted by fractioll~ whe!'e tlit' integer part of the hut' index denotes the n('alT~t IOWt'r ha:;ic hut' and tht; frac- tion part entering in the huc A Ai 0 re:;ulb by additiyd~-mixing 0 time:- the limit hue Ai+1 with (1 ft) time" the limit hue ---1;, Identical COLOROID saturation is attrihutcd to colours resulting from equal percentages of a limit colour with any pcrcentage of absolute white and ahsolute black, nUllH'rically expresscd as product of the saturation of the limit colour hy the perc('ntag(':

T pT; .. (17)

By ddillitiull, lit(' COLOROID saturatioll of 111(, limi1 colour j" IOU, those of absolute white and absolute black are ZlTO, thus:

T;.

=

100; 0;

O.

(18)

COLOROID saturation of a coluur ean abo \)(' expn',;:-;('t! In- Iht, ~atura­

tion of a more saturav'd surface colour of ('qual huf':

T PtTIi.' (19)

COLOROID hrighlllt'';,;(,:, an' ('qual for llllllH·rically ('qual tri:,limulut' yalut's Y, cOllvt'l'tl'd to COLOROID brightne",:,;

v =

10 \ Y, (20)

"'quare root of 100 time:, the eIE tristimulu:3 '-aInt, Y.

The COLOROID brightIless of allsoll1t(' whitt, i" 100, thaL of ah"olult·

black is z(~ro, i.p.:

100;

O.

(21)

Th(~ COLOROID hrightllt'SS of a eolour i" tell times the squal't' root of perCl'lltage sums of tristilllulus yalue:, Y of its limit colour, of ahsolute white and absolut(; black. Written in terms ofEqs (3), (13) and (15):

v

= 10 YpYi.

+

100w (22)

(21)

or, using tristimulus values Y- of a surface colour of the same eOLOROID hue but higlwr COLOROID saturation, of a real "whiti' and a rt'al hlack:

v

= 10 \ Pt is' (23)

3.3 COLOROID colollr codes

Thrce num}JPrs are W'wd to identifv a colonr in thf' eOLOROID 5vstt'111.

. .

First of tht'se rd!'rs to the' eOLOROID hue A, tht' spcond to the eOLOROID

;:aturatinn T and tIlt' third to the eOLOROID hrightlle;:" V, always in this

;;equence.

The colour of eOLOROID hUt, 13, eOLOROID saturation 22 and eOLO- ROID hrightllf'SS 56 is thus codt·t1 as 13-22-56, and another colour coded

12-22-56 is mOl"(' green;

14·-22-56 is nUH"(' orangt·;

13-21-56 is less :"aturatf'd;

13-23-56 iF lllore saturatt·tl:

13-22-55 is darker;

13-22-57 is brighter.

3.4 Conversion be/lceen COLOROID codes and CIE tristimullls values

eIE and eOLOROID systt<I1lS are ill an unambiguous relationship so that eOLOROID codes of the colour spact' and eIE co-oHlinatt'5 are easy to convert into each other in eitllt'r direction.

Conversion from eIE XYZ system to COLOROID starts from given x, y, Y to calculate tllt' A, T, V valucs.

The eOLOROID hue is rt~ad offthf~ table oflimit culours with Ll}. 11lln steps applying Eq. (16):

If lwces;:ary, linear interpolation lllay be used.

The eOLOROID saturation is calculated from the following rquation~

by using Eqs (2) and (3), taking also Eq. (14) into consideration. Eqs (24) rcsulted from the well-known formula of tht' XYZ system and the definition of 8 in section 3.2:

x.

= X}.8}.:

I. 100-

Y _ y}.8}..

t. - 100 '

(24.) Y _ Y o8w •

w - ,

100

(22)

56 NEMCSICS

After substitutions:

x _

pXi. Cl.

+

WXo Cw •

- 100 '

y = PYi. ci.

+

wyo clll •

100 (25)

Again substituting (24), (25) and (5) into the standard formulae of the XYZ system involving c:

x Y

x

=

100- and Y

=

100-

C C

expresses CIE chromaticity co-ordinates in terms of COLOROID colour com- ponents:

(26)

Expressing w from Eq. (3) in respect of (13) and (15):

Y-pY-

W = f.

100 (27)

'which substituted into Eq. (26), expressing P, yields:

(28) and

(29)

Substituting (29) into (17) and taking (18) into consideration yidds the COLO- ROID saturation:

(30) or

(31)

The values of Xi., )'i.' Y;. and Ci. are found in the COLOROID tables for limit colours with Lt}. = 1 nm steps, namely: Xi. = f(tg cp); )'i. = f(tg cp);

Yi. = f(tg cp); c;. f(tg cp).

(23)

The COLOROID brightness is calculated using Eq. (20).

Conversion from the COLOROID system into the CIE XYZ system IS

sho·wn on the example of calculating x, y, Y from given A, T, V values.

Expressing x and y from Eqs (30) and (31):

and

Expressing Y from Eq. (20), and knowing that Y;. = 100

Y;.,

these values are substituted into the former equations to yield:

x= cWXO(V2 - 100 TYt.)

+

100Tct.xt.

cw(V2 -100Tyt.)

+

100Tct. (32)

(33)

Xi.' Xi. and Si. are again read off the dJ. = I nm tables of the COLOROID limit colours, namely Xi. =f(A);

y;.

=f(A); and e;. =f(A), hence

( V)2

Y=

10 .

(34)

Fig. 14. Cylindrical surfaces containing colours of lYlunsell chroma 4, 8, 12 in the iVlunsell colour solid

(24)

58 NEMCSICS

T

Fig. 15. Conic surfaces containing colours of Munsell chroma 4, 8, 12 in the COLOROID solid

3.5 Comparison of COLOROID with other colour systems

COLOROID co-ordinates of every sample of the Munsell colour collec- tion - practically considered as reference in determining perceptually even colour differences and widely used, have been calculated and tabulated. Figs 14, 15, 16 and 17 truly reflect the saturation differences between the two systems.

_---:3"\'<;::::::---j70

Fig. 16. Cylindrical surfaces containing colours of COLOROID saturation T = 20, 30, 40 in the COLOROID colour solid

(25)

Fig. 17. Conic surfaces containing colours of COLOROID saturation T = 20, 30, 40 in the Munsell colour solid

Also COLOROID co-ordinates of the samples of the DIN colour collec- tion have been tabulated.

The Tables showing the 3072 perceptually equidistant COLOROID colour points expressed in the CIE 1931 XYZ system, the CIELUV and CIELAB systems are rather instructive. Figs 18, 19, 20, 21 drawn from these Tables truly reflect the differences between these colour spaces.

Fig. 18. Cylindrical surfaces containing colours of COLOROID saturation T = 10, 20, 30, 40 in the COLOROID colour space

(26)

60

VA

100

NEJICSICS

Fig. 19. Conic surfaces containing colours';of COLOROID saturation T = 20, 30, 40 in the

L CIE 1931 colour space

Fig. 20. Conic surfaces containing colours of COLOROID saturation T = 20, 30, 40 in the CIEL "{TV colour space

Fig. 21. Conic surfaces containing colours of COLOROID saturation T = 20, 30, 40 in the CIELAB colour space

(27)

Fig. 22 is a comparison between gray scales of the lllunsell system, the Color Harmony lVlanual, the DIN system and the COLOROID.

v!

,r I ,

o 20 L,() 60 80 'KXJ~

Fig. 22. Comparison of gray scales according to DIN (Richter 1953), Color Harmony l'vIanual (Foss 1944), lvlunsell (Newhall 1943, Ladd and Pinney 1955) and COLOROID (Nemcsics,

Beres 1974)

4. The architectural use of the COLOROID codes

The COLOROID codes may have manifold uses in architectural design and construction.

These codes unambiguously identify the colours, permit them to be visualized and e::timated in their setting. The code system points to the corn- positional relations between colours, of great architectural importance, it suits to describe and even visualize them.

4.1 Colour trueness evaluation

The even changes in COLOROID codes correspond to even changes in the colours they represent. Therefore COLOROID codes suit evaluation of the trueness of the colour. Its adoption both by designers and hy manufacturers of building materials and paints 'would simplify to state adherence to the design and the degrcc and direction of deviations.

Recently the system has heen introduced both in design and in construc- tion. At a difference from other industries, in the building industry colour deviations "were found to be inadequately described by onc colour difference value. Maximum diffcrence in the hue must not exceed one COLOROID hue unit, saturation and brightness differences 5 COLOROID saturation or 5 COLOROID brightness units [22, 23, 32, 34, 36].

(28)

62 lYEMCSICS

4.2 Reference data in colour design

Experiments on the man to colour relation are very important for the colour design.

Colour-dynamical experiments on the man to colour relation have been carried out at the Technical University, Budapest since the early sixties. Investigations concerning colour preferences of different age groups, associations, colour effects on space and mass perception, physiological effects, etc. have been related to COLOROID codes. Generalizing our results has led to develop a COLOROID colour-dynamical design aid, involving a system of colour harmony relations based on COLOROID codes [24 to 31].

4.3 Visualization of the proposed colour

An important feature of COLOROID is the possibility to convert its codes into colour-mixing components permitting the designer to reproduce any surface colour on a Maxwell disc using a disc of the desired hue or two chromatic sample discs deviating by less than rp

=

30° on either side from the colour-space location of the hue of the colour to be reproduced, a white and a black disc [33,35]. The rotating disc has to be covered by Pt% of the chromatic, by St% of the black sample. Mixing percentages are from Eq. (19):

from Eq. (23):

and from Eq. (6):

Pt=--; T Ttp

4.4 Formulation of colour composition relations

(35)

(36)

(37)

Designers are often facing the problem to design a colour composition taking the colour features of a given building or cladding material into consider- ation. In the following, some examples will be presented on how to determine the colours fitting the features.

First example: Given are the colours of two coating materials. Both colours are of the same hue but of greatly different saturation and brightness. These features are to be involved to produce an interior ,~ith colours of the same hue with the specific monochromatic atmosphere.

Be the two colours coded as:

(29)

The designer plans to use other n colours in the same space. These n surface colours should be of the same hue as the two pre-existing ones but of saturations and brightnesses intermediary between both so as to produce a harmonic scale.

A - T - V 26 ~ 6 - 55 26 - 9 - 70

0"

,26 - 12 - 75 26.,. 15 - BO 2{\ - 18 -85

vi

90 -:-....,.

-...

~ ~'

80

/ / V

70

6 12 le 24

Il>T

Fig. 23. Colours forming a harmonic series in the A = 26 COLOROID hue plane From our great many experiments it can be concluded that in general, colours along a straight line in the COLOROID hue plane are felt as harmonic (Fig. 23). Saturation and bright- ness differences between the n -+-2 members of this colour scale for Tb > Ta and Vb > Va are:

to be coded as:

Fa (A, Ta' Va)

Fa-+-l (A, Ta

+

qT' Va

+

qv)

Fa-+-2 (A, Ta

+

2qT' Va

+

2qv)

Fa+n (A, Ta

+

nqT' Va

+

nqv)

Fb (A, Tb' Vb)'

To reproduce the colours in the scale, a colour of the same hue but of higher saturation, with CIE XYZ or COLOROID codes, a white and a black surface are needed. Be the codes of the chromatic surface:

of the white surface:

and of the black surface:

(30)

64 NEMCSICS

The colour components af point Fa+n will be determined as follows. The proportion of the chromatic surface on the Maxwell disc is, according to Eq. (35):

Ta+nqT

Pt= T

tp

the proportion of the white surface is given by Eq. (36):

and of the black one by Eq. (37):

Second example: There are given two colours with complementary hues and a third colour of intermediary saturation and brightness, and either of the same hue as one of the two former or an achromatic colour is sought for.

First, the COLOROID co-ordinates of point Q on the line connecting the complementary colour points P and R have to be determined.

Hence and

P(Ap, T p' Vp)

R(AR' TR, VR) are given;

Q(A Q, T Q, VQ) is sought for.

Let us take an amount (3 from colour P and an amount (1 - (3) from colour R assuming

o ;;;;;

f3 ;;;;; 1. The COLOROID co-ordinates of the mixed colour Q are

For for

TQ = (3Tp - (1 - (3) TR,

VQ = 10

V

f3 (

~~ r +

(1 - f3)

(~~ r

AQ = Ap, AQ = AR ,

for T Q = 0, the colour is an achromatic one.

From these data the COLOROID components of colour Q can be computed using Eqs (35), (36) and (37), and the colour Q can be reproduced on the lvIaxwell disc. Diametral scales produced by mixing complementary colours are seen in Fig. 24 in COLOROID sections, COLOROID co-ordinates of the scale members can be approximated by graphical means as well. The heavy continuous line in the horizontal section represents the saturation of the most saturated pigment colours.

Third example: Two separate colours are given, differing by hue, by saturation and by brightness. The designer fancies to insert further colours intermediary between the former for all three colour parameters so as to produce a harmonic series. In the following, a single colour in this imaginary scale between the two pre-existing ones will be determined.

First, the COLOROID co-ordinates of the new colour have to be determined. Given are the COLOROID co-ordinates of colours VI and F2 :

Fl(Al , T l , VI) where Al =f(rpl) and F2(A 2, T2, V2) where A2 =f(rp2)'

(31)

_ - - ' _ - ' - _ - L _ - j BC -+-+--1---+---+-"*,,'---'-

Fig. 24. Diametral scales produced by mixing complementary colours. fhe heavy continuous line shows the COLOROID saturation ...-alnes of the most saturated pigment colours

COLOROID co-ordinates

F(A. T. V) where A = f(rr) of colour F are wanted.

An amount fJ of colour F, and an amonnt 1 - /1 of colour F~ are mixed to get colour F, assuDling 0 :;; {3 ~ 1.

The needcd equations are deduced by changing first from the COLOROID polar co- ordinate system to the Cartesian co-ordinate system (Fig. 25). Parameters of colours F, and F~

will be Il" r" n , andll~, v~, n~, resp. As all the Tvalues are contained in the planc ll, v in con- formity with Fig. 25:

II /3 T, cos 'Pl -;-(1 /3) T2 cos rp~

fJ) T2 sin 'P~.

Returning to polar co-ordinates, it is written:

T=Yll~+V" and tgrp=~. v

5 Periodica Polytechnic. A. 23fl

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